We briefly review the observation model in [1]} for generating the simulated dataset for training. Denote the impulse response function of the pulsed light as \(s(t)\) , and \(n_{b}\)  denotes the average noise intensity including the background light and dark count of SPAD. For the (\(i,j\) )-th pixel, the photon detections produced by SPAD can be modelled by an inhomogeneous Poisson process [2]} with the time-varying rate function as

ij(t) = ij s(t - 2Zijc) + nb,

where \(\mathrm {c}\)  is the speed of light and \(\alpha _{ij}\)  is the light energy attenuation ratio due to atmospheric attenuation and diffuse reflection. \(\eta \)  is the quantum efficiency of the detector. Based on the rate function, the expectation value of the detected photon counts at the (\(i,j\) )-th pixel during an integration period \(\Delta \)  is calculated by

Eij (Tb, Tb + ) = TbTb +  ij(t)dt,

where \(T_{b}\)  denotes the beginning time of the integration period. Since the detection of each photon is independent of each other, the photon counting histogram of the (\(i,j\) )-th pixel based on \(N\)  illuminations can be sampled by following Poisson process as
\(h_{ijk} \sim \mathrm {Poisson}(N \cdot \mathrm {E}_{ij}(k\Delta ,(k+1)\Delta )), \quad k = 1,2 \cdots ,T.\) 
